The .50 Cal Browning - which is almost 40 years old - was mounted on an Army vehicle.
A senior officer stationed at the Joint Special Operations Command HQ in Kabul gave the go-ahead for the kill.
One source told the paper a special sight was fitted on the machine gun and a spotter then estimated wind speed.
"He also took into account the heat of the day and the light," they said. "The image of his target was quite "watery" because of the heat being given off from the ground."
The Islamic State fighter seemed to be briefing his men as he stood addressed fighters for about 20 minutes.
"It took several seconds for the round to hit the commander who appeared to fl y into several pieces. For a few seconds no-one moved. When they realised what had happened they got up and ran away."
The paper reports that the kill is thought to have saved more than 20 lives. The gun was used as a long-range weapon in the 1950s during the Korean War.
This feat is believed to be the first time the machine gun has been used for a sniper hit by the SAS.